Loss-in-weight Feeder Calculations

Loss-in-Weight Feeder Calculator | Industrial Processing Tools :root { –primary-color: #004a99; –secondary-color: #003366; –success-color: #28a745; –bg-color: #f8f9fa; –text-color: #333; –border-color: #dee2e6; –white: #ffffff; } * { box-sizing: border-box; margin: 0; padding: 0; } body { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, sans-serif; line-height: 1.6; color: var(–text-color); background-color: var(–bg-color); } .container { max-width: 960px; margin: 0 auto; padding: 20px; } /* Header Styles */ header { text-align: center; margin-bottom: 40px; padding: 40px 0; background: var(–white); border-bottom: 1px solid var(–border-color); } h1 { color: var(–primary-color); font-size: 2.5rem; margin-bottom: 10px; } .subtitle { color: #666; font-size: 1.1rem; } /* Calculator Styles */ .calc-wrapper { background: var(–white); padding: 30px; border-radius: 8px; box-shadow: 0 4px 6px rgba(0,0,0,0.05); margin-bottom: 50px; border: 1px solid var(–border-color); } .input-section { margin-bottom: 30px; } .input-group { margin-bottom: 20px; } .input-group label { display: block; font-weight: 600; margin-bottom: 8px; color: var(–secondary-color); } .input-group input, .input-group select { width: 100%; padding: 12px; border: 1px solid var(–border-color); border-radius: 4px; font-size: 16px; transition: border-color 0.3s; } .input-group input:focus { outline: none; border-color: var(–primary-color); box-shadow: 0 0 0 3px rgba(0, 74, 153, 0.1); } .helper-text { font-size: 0.85rem; color: #6c757d; margin-top: 5px; } .error-msg { color: #dc3545; font-size: 0.85rem; margin-top: 5px; display: none; } .btn-group { display: flex; gap: 15px; margin-top: 20px; } button { padding: 12px 24px; border: none; border-radius: 4px; font-size: 16px; font-weight: 600; cursor: pointer; transition: background-color 0.2s; } .btn-reset { background-color: #6c757d; color: white; } .btn-copy { background-color: var(–success-color); color: white; } .btn-reset:hover { background-color: #5a6268; } .btn-copy:hover { background-color: #218838; } /* Results Styles */ .results-section { background-color: #f1f8ff; padding: 25px; border-radius: 6px; border-left: 5px solid var(–primary-color); margin-top: 30px; } .main-result { text-align: center; margin-bottom: 25px; padding-bottom: 20px; border-bottom: 1px solid #d1e3f5; } .main-result-label { font-size: 1.1rem; color: var(–secondary-color); margin-bottom: 10px; } .main-result-value { font-size: 2.5rem; font-weight: 700; color: var(–primary-color); } .intermediate-results { display: flex; flex-wrap: wrap; gap: 20px; justify-content: space-between; } .result-item { flex: 1 1 45%; background: white; padding: 15px; border-radius: 4px; box-shadow: 0 2px 4px rgba(0,0,0,0.05); } .result-item label { display: block; font-size: 0.9rem; color: #666; margin-bottom: 5px; } .result-item span { font-size: 1.2rem; font-weight: 600; color: #333; } /* Table & Chart */ .data-visuals { margin-top: 30px; } table { width: 100%; border-collapse: collapse; margin-bottom: 30px; background: white; } th, td { padding: 12px; text-align: left; border-bottom: 1px solid var(–border-color); } th { background-color: var(–primary-color); color: white; } .chart-container { background: white; padding: 20px; border: 1px solid var(–border-color); border-radius: 4px; margin-top: 20px; position: relative; height: 350px; } canvas { width: 100%; height: 100%; } .chart-legend { text-align: center; margin-top: 10px; font-size: 0.9rem; color: #666; } /* Article Styles */ article { background: var(–white); padding: 40px; border-radius: 8px; box-shadow: 0 4px 6px rgba(0,0,0,0.05); border: 1px solid var(–border-color); } article h2 { color: var(–primary-color); margin-top: 40px; margin-bottom: 20px; font-size: 1.8rem; border-bottom: 2px solid #f0f0f0; padding-bottom: 10px; } article h3 { color: var(–secondary-color); margin-top: 25px; margin-bottom: 15px; font-size: 1.4rem; } article p { margin-bottom: 15px; color: #444; } article ul, article ol { margin-bottom: 20px; padding-left: 25px; } article li { margin-bottom: 8px; } .variable-table { width: 100%; margin: 20px 0; border: 1px solid var(–border-color); } .variable-table th { background-color: #f1f8ff; color: var(–primary-color); } .faq-item { margin-bottom: 20px; background: #f8f9fa; padding: 20px; border-radius: 6px; } .faq-question { font-weight: 700; color: var(–primary-color); margin-bottom: 10px; display: block; } .internal-links { background-color: #e9ecef; padding: 20px; border-radius: 6px; margin-top: 40px; } .internal-links a { color: var(–primary-color); text-decoration: none; font-weight: 600; } .internal-links a:hover { text-decoration: underline; } footer { text-align: center; padding: 40px 0; color: #666; font-size: 0.9rem; margin-top: 40px; } @media (max-width: 600px) { .intermediate-results { flex-direction: column; } h1 { font-size: 2rem; } article { padding: 20px; } }

Loss-in-Weight Feeder Calculator

Optimize your gravimetric feeding process and refill strategies

The desired mass flow rate of material leaving the feeder.
Please enter a valid positive feed rate.
Density of the material in loose bulk form (e.g., pellets, powder).
Please enter a valid positive density.
Total internal volume of the weigh hopper.
Please enter a valid positive volume.
Rate at which the refill device fills the hopper (must be > Feed Rate).
Refill rate must be greater than feed rate.
Percentage of capacity where refill triggers.
Percentage of capacity where refill stops.
High level must be greater than low level.
Time Between Refills (Gravimetric Mode)
— min
Duration the feeder operates in true gravimetric mode before needing a refill.
— sec
— kg
— cycles/hr
— kg

Cycle Analysis Table

Parameter Value Unit

Hopper Weight vs. Time (Simulation)

— Weight Profile | — High Limit | — Low Limit

What are Loss-in-Weight Feeder Calculations?

Loss-in-weight feeder calculations are the mathematical processes used to size, configure, and optimize gravimetric feeding systems in industrial manufacturing. A loss-in-weight (LIW) feeder operates by weighing the entire feeding system (hopper, material, and metering device) and measuring the rate at which weight decreases over time.

These calculations are critical for process engineers to ensure that the feeder can maintain the target mass flow rate without interruption. By accurately calculating variables such as refill frequency, usable hopper capacity, and refill duration, manufacturers can prevent process instability, material bridging, or "starving" the downstream extruder or mixer.

Common industries utilizing these calculations include plastics compounding, food processing, pharmaceutical manufacturing, and chemical processing, where precise ingredient ratios are mandatory for product quality.

Loss-in-Weight Feeder Formula and Explanation

The core principle of a loss-in-weight feeder is derived from the change in weight ($\Delta W$) over a change in time ($\Delta t$). The controller adjusts the speed of the metering device (screw or vibratory tray) to keep this rate constant.

Core Formula

The mass flow rate ($\dot{m}$) is calculated as:

Rate (kg/hr) = (Weight at Time T1 – Weight at Time T2) / (T2 – T1)

Refill Logic Formulas

Since the hopper has a finite capacity, it must be refilled periodically. The system typically switches to "volumetric mode" during refill. The key calculations for sizing the cycle are:

  • Usable Batch Weight: $W_{batch} = V_{hopper} \times \rho_{bulk} \times (High\% – Low\%)$
  • Gravimetric Time (Run Time): $t_{run} = W_{batch} / \dot{m}_{feed}$
  • Net Refill Rate: $\dot{m}_{net} = \dot{m}_{source} – \dot{m}_{feed}$
  • Refill Time: $t_{refill} = W_{batch} / \dot{m}_{net}$
Variable Meaning Unit Typical Range
$\dot{m}_{feed}$ Target Feed Rate kg/hr 0.5 – 5000+
$\rho_{bulk}$ Bulk Density kg/m³ 200 – 1500
$V_{hopper}$ Hopper Volume Liters 10 – 5000
$\dot{m}_{source}$ Refill Source Rate kg/hr 5x – 10x Feed Rate

Practical Examples of Feeder Calculations

Example 1: Plastic Pellet Extrusion

A plastics manufacturer needs to feed polyethylene pellets into an extruder at 100 kg/hr. The pellets have a bulk density of 550 kg/m³. They use a 200-liter hopper with refill setpoints at 20% and 80%.

  • Total Capacity (Mass): 200 L × 0.55 kg/L = 110 kg
  • Usable Batch: 110 kg × (0.80 – 0.20) = 66 kg
  • Time Between Refills: 66 kg / 100 kg/hr = 0.66 hours (39.6 minutes)

Interpretation: The system runs stably for nearly 40 minutes between refills, which is excellent for accuracy.

Example 2: Fine Powder Additive

A chemical process requires a fine powder additive at 20 kg/hr. The density is light (300 kg/m³). The hopper is small (50 Liters). The refill source is slow, only providing 40 kg/hr.

  • Total Capacity: 50 L × 0.3 kg/L = 15 kg
  • Usable Batch: 15 kg × 0.60 (60% swing) = 9 kg
  • Net Refill Rate: 40 kg/hr (source) – 20 kg/hr (feed) = 20 kg/hr
  • Refill Time: 9 kg / 20 kg/hr = 0.45 hours (27 minutes)

Interpretation: This setup is problematic. The refill takes 27 minutes, during which the feeder is in volumetric mode (blind). The refill source rate should be increased significantly to minimize blind time.

How to Use This Loss-in-Weight Feeder Calculator

  1. Enter Target Feed Rate: Input the required process rate in kg/hr.
  2. Input Material Properties: Enter the bulk density. If unknown, weigh a known volume (e.g., a 1-liter cup) to estimate.
  3. Define Hopper Geometry: Input the total volume of the hopper in Liters.
  4. Set Refill Parameters: Input the rate at which your refill system (vacuum loader, slide gate) delivers material.
  5. Adjust Setpoints: Define the Low and High level percentages. Standard practice is often 20% Low and 80% High.
  6. Analyze Results: Look at the "Refill Duration." If this time is too long relative to the "Time Between Refills," your accuracy may suffer.

Key Factors That Affect Feeder Results

Several physical and operational factors influence the accuracy of loss-in-weight feeder calculations:

  • Material Bulk Density Variations: If density changes during the process, the volumetric backup mode during refill will be inaccurate.
  • Refill Rate Speed: A slow refill extends the time the feeder operates without gravimetric feedback. Ideally, refill should be 10x faster than the feed rate.
  • Venting and Air Pressure: Rapid refills can aerate powders, causing them to flush through the screw like a liquid. Proper venting is essential.
  • Vibration Interference: External vibrations can corrupt the weight signal, causing the controller to react to noise rather than weight loss.
  • Material Bridging: If material sticks to the hopper walls (rat-holing), the effective volume decreases, increasing refill frequency unexpectedly.
  • Minimum Weighment: The usable batch weight must be large enough for the load cells to resolve accurately. Very short cycles reduce accuracy.

Frequently Asked Questions (FAQ)

What is the ideal refill frequency for a loss-in-weight feeder?

Generally, a refill cycle every 10 to 60 minutes is acceptable. If refilling occurs every 2 minutes, the system spends too much time settling and refilling, reducing overall accuracy.

Why is the refill rate important?

During refill, the feeder locks the screw speed (volumetric mode). If the refill takes too long, the feeder cannot correct for density changes, leading to feed rate errors.

Can I use this calculator for liquid loss-in-weight?

Yes, the math is identical. Simply use the liquid's density and the tank volume. Ensure the units (kg/L) are consistent.

What happens if the refill rate is lower than the feed rate?

The hopper will never fill up. The system will eventually run empty and alarm. The refill source must always exceed the target feed rate.

How do I calculate bulk density?

Weigh a known volume of material. Formula: Density (kg/m³) = Weight (kg) / Volume (m³). Note that 1000 Liters = 1 m³.

What is "Turndown Ratio"?

It is the ratio between the maximum and minimum controllable feed rates. A high turndown ratio means the feeder is flexible for different products.

Does this calculator account for "heel" weight?

The "Low Level Setpoint" acts as the heel (material left in the bottom). We calculate usable weight based on the difference between High and Low setpoints.

Why does the weight reading fluctuate?

Vibration, air currents, or flexible connections that are too stiff can cause weight signal noise. Digital filtering in the controller usually handles this.

© 2023 Industrial Processing Tools. All rights reserved.
Disclaimer: This calculator is for estimation purposes only. Always consult equipment manuals for precise specifications.

// Initialize calculator on load window.onload = function() { calculateLIW(); }; function calculateLIW() { // 1. Get Inputs var feedRate = parseFloat(document.getElementById('feedRate').value); var bulkDensity = parseFloat(document.getElementById('bulkDensity').value); var hopperVolume = parseFloat(document.getElementById('hopperVolume').value); var refillRate = parseFloat(document.getElementById('refillRate').value); var lowLevel = parseFloat(document.getElementById('lowLevel').value); var highLevel = parseFloat(document.getElementById('highLevel').value); // 2. Validation Flags var isValid = true; // Reset errors document.getElementById('feedRateError').style.display = 'none'; document.getElementById('densityError').style.display = 'none'; document.getElementById('volumeError').style.display = 'none'; document.getElementById('refillRateError').style.display = 'none'; document.getElementById('levelError').style.display = 'none'; // Validate if (isNaN(feedRate) || feedRate <= 0) { document.getElementById('feedRateError').style.display = 'block'; isValid = false; } if (isNaN(bulkDensity) || bulkDensity <= 0) { document.getElementById('densityError').style.display = 'block'; isValid = false; } if (isNaN(hopperVolume) || hopperVolume <= 0) { document.getElementById('volumeError').style.display = 'block'; isValid = false; } if (isNaN(refillRate) || refillRate <= feedRate) { document.getElementById('refillRateError').style.display = 'block'; isValid = false; } if (highLevel <= lowLevel) { document.getElementById('levelError').style.display = 'block'; isValid = false; } if (!isValid) return; // 3. Calculations // Convert density to kg/L (since volume is in Liters) // 1 kg/m^3 = 0.001 kg/L var densityKgL = bulkDensity / 1000; // Total Mass Capacity of Hopper var totalMassCapacity = hopperVolume * densityKgL; // Mass at High and Low Levels var massHigh = totalMassCapacity * (highLevel / 100); var massLow = totalMassCapacity * (lowLevel / 100); // Usable Batch Weight var usableBatchWeight = massHigh – massLow; // Time Between Refills (Gravimetric Run Time) // Time = Mass / Rate var runTimeHours = usableBatchWeight / feedRate; var runTimeMinutes = runTimeHours * 60; // Refill Calculation // Net Refill Rate = Source Rate – Feed Rate (because feeding continues during refill) var netRefillRate = refillRate – feedRate; // Refill Time var refillTimeHours = usableBatchWeight / netRefillRate; var refillTimeSeconds = refillTimeHours * 3600; var refillTimeMinutes = refillTimeHours * 60; // Total Cycle Time var totalCycleTimeMinutes = runTimeMinutes + refillTimeMinutes; // Refill Frequency (Cycles per hour) var cyclesPerHour = 60 / totalCycleTimeMinutes; // 4. Update UI Results document.getElementById('timeBetweenRefills').innerText = runTimeMinutes.toFixed(2) + " min"; document.getElementById('refillDuration').innerText = refillTimeSeconds.toFixed(1) + " sec"; document.getElementById('batchWeight').innerText = usableBatchWeight.toFixed(2) + " kg"; document.getElementById('refillFreq').innerText = cyclesPerHour.toFixed(1) + " cycles/hr"; document.getElementById('massCapacity').innerText = totalMassCapacity.toFixed(2) + " kg"; // Update Table var tableBody = document.getElementById('resultsTableBody'); tableBody.innerHTML = ` Total Hopper Capacity${totalMassCapacity.toFixed(2)}kg Usable Batch Weight${usableBatchWeight.toFixed(2)}kg Gravimetric Run Time${runTimeMinutes.toFixed(2)}min Refill Time${refillTimeSeconds.toFixed(1)}sec Total Cycle Time${totalCycleTimeMinutes.toFixed(2)}min Net Refill Rate${netRefillRate.toFixed(1)}kg/hr `; // 5. Draw Chart drawChart(massHigh, massLow, runTimeMinutes, refillTimeMinutes); } function drawChart(high, low, runTime, refillTime) { var canvas = document.getElementById('feederChart'); var ctx = canvas.getContext('2d'); // Handle DPI for crisp rendering var dpr = window.devicePixelRatio || 1; var rect = canvas.getBoundingClientRect(); canvas.width = rect.width * dpr; canvas.height = rect.height * dpr; ctx.scale(dpr, dpr); var width = rect.width; var height = rect.height; var padding = 40; // Clear canvas ctx.clearRect(0, 0, width, height); // Determine scales // Y axis: 0 to High * 1.1 var maxY = high * 1.1; // X axis: Show 2 full cycles var cycleTime = runTime + refillTime; var totalXTime = cycleTime * 2.2; // Show slightly more than 2 cycles // Helper to map values to pixels function mapX(t) { return padding + (t / totalXTime) * (width – 2 * padding); } function mapY(w) { return height – padding – (w / maxY) * (height – 2 * padding); } // Draw Axes ctx.beginPath(); ctx.strokeStyle = '#ccc'; ctx.lineWidth = 1; // Y Axis ctx.moveTo(padding, padding); ctx.lineTo(padding, height – padding); // X Axis ctx.moveTo(padding, height – padding); ctx.lineTo(width – padding, height – padding); ctx.stroke(); // Draw Limit Lines (High and Low) ctx.setLineDash([5, 5]); // High Limit ctx.beginPath(); ctx.strokeStyle = '#28a745'; ctx.moveTo(padding, mapY(high)); ctx.lineTo(width – padding, mapY(high)); ctx.stroke(); ctx.fillStyle = '#28a745'; ctx.fillText("High: " + high.toFixed(1) + "kg", width – padding – 70, mapY(high) – 5); // Low Limit ctx.beginPath(); ctx.strokeStyle = '#dc3545'; ctx.moveTo(padding, mapY(low)); ctx.lineTo(width – padding, mapY(low)); ctx.stroke(); ctx.fillStyle = '#dc3545'; ctx.fillText("Low: " + low.toFixed(1) + "kg", width – padding – 70, mapY(low) – 5); // Draw Sawtooth Wave ctx.setLineDash([]); ctx.lineWidth = 2; ctx.strokeStyle = '#004a99'; ctx.beginPath(); var t = 0; var currentWeight = high; ctx.moveTo(mapX(t), mapY(currentWeight)); // Simulate 3 cycles for (var i = 0; i < 3; i++) { // Feeding Phase (Weight goes down) t += runTime; currentWeight = low; ctx.lineTo(mapX(t), mapY(currentWeight)); // Refill Phase (Weight goes up) t += refillTime; currentWeight = high; ctx.lineTo(mapX(t), mapY(currentWeight)); } ctx.stroke(); // Labels ctx.fillStyle = '#333'; ctx.font = '12px Arial'; ctx.fillText("Time (min)", width / 2, height – 10); ctx.save(); ctx.translate(15, height / 2); ctx.rotate(-Math.PI / 2); ctx.fillText("Hopper Weight (kg)", 0, 0); ctx.restore(); } function resetCalculator() { document.getElementById('feedRate').value = 50; document.getElementById('bulkDensity').value = 600; document.getElementById('hopperVolume').value = 100; document.getElementById('refillRate').value = 500; document.getElementById('lowLevel').value = 20; document.getElementById('highLevel').value = 80; calculateLIW(); } function copyResults() { var feedRate = document.getElementById('feedRate').value; var time = document.getElementById('timeBetweenRefills').innerText; var refill = document.getElementById('refillDuration').innerText; var batch = document.getElementById('batchWeight').innerText; var text = "Loss-in-Weight Feeder Calculation Results:\n"; text += "Target Feed Rate: " + feedRate + " kg/hr\n"; text += "Time Between Refills: " + time + "\n"; text += "Refill Duration: " + refill + "\n"; text += "Usable Batch Weight: " + batch + "\n"; var tempInput = document.createElement("textarea"); tempInput.value = text; document.body.appendChild(tempInput); tempInput.select(); document.execCommand("copy"); document.body.removeChild(tempInput); var btn = document.querySelector('.btn-copy'); var originalText = btn.innerText; btn.innerText = "Copied!"; setTimeout(function(){ btn.innerText = originalText; }, 2000); }

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